zbMATH — the first resource for mathematics

Error analysis and determination of the scaling constant for the scaling power method. (Chinese) Zbl 0647.65031
The scaling power method discussed intensively by R. C. Ward [SIAM J. numer. Anal. 14, 600-610 (1977; Zbl 0363.65031)] is one of the most efficient methods for computing the matrix exponential $$e^{At}$$ which is implemented through converting $$e^{At}$$ into $$[e^{At/N}]^ N$$. In this paper, an appropriate choosen interval for N is given. A skip product method to overcome the difficulty of huge amount of computation and the error analysis of the method are advanced. A numerical example of an ill-conditioned differential equation with the rigidity ratio $$10^ 6$$ is included.
Reviewer: Wang Chengshu
MSC:
 65F30 Other matrix algorithms (MSC2010) 65L05 Numerical methods for initial value problems involving ordinary differential equations